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 A134939 Numerator of the expected number of random moves in Tower of Hanoi problem with n disks starting on peg 1 and ending on peg 3. 3
 0, 2, 64, 1274, 21760, 348722, 5422144, 83000234, 1259729920, 19027002722, 286576949824, 4309163074394, 64731832372480, 971825991711122, 14585021567101504, 218843984372767754, 3283277591489597440, 49254723695591689922, 738870890792896773184, 11083513664870504400314 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Both allowable transitions out of any of the three special states in which all the disks are on one of the pegs have probability 1/2 and each of the three allowable transitions out of any of the other 3^n - 3 states have probability 1/3. LINKS Towers of Hanoi with random moves, mersenneforum.org M. A. Alekseyev and T. Berger, Solving the Tower of Hanoi with Random Moves. In: J. Beineke, J. Rosenhouse (eds.) The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Princeton University Press, 2016, pp. 65-79. ISBN 978-0-691-16403-8 Index entries for linear recurrences with constant coefficients, signature (32,-342,1440,-2025). FORMULA a(n) = numerator(e(n)) with e(n) defined below. e(n) = (3^n-1)*(5^n-3^n) / (2*3^(n-1)), a(n) = (3^n-1)*(5^n-3^n) / 2. - Max Alekseyev, Feb 04 2008 G.f.: -2*x*(45*x^2-1) / ((3*x-1)*(5*x-1)*(9*x-1)*(15*x-1)). - Colin Barker, Dec 26 2012 EXAMPLE The values of e(0), ..., e(4), e(5) are 0, 2, 64/3, 1274/9, 21760/27, 348722/81. CROSSREFS Cf. A007798, A134940. Sequence in context: A299724 A047707 A223121 * A217268 A122603 A127691 Adjacent sequences: A134936 A134937 A134938 * A134940 A134941 A134942 KEYWORD nonn,frac,easy AUTHOR Toby Berger (tb6n(AT)virginia.edu), Jan 23 2008 EXTENSIONS Values of e(5) onwards and general formula found by Max Alekseyev, Feb 02 2008, Feb 04 2008 Shorter name by Michel Marcus, Dec 27 2012 STATUS approved

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Last modified December 2 07:55 EST 2022. Contains 358493 sequences. (Running on oeis4.)